Great question. Engine building is a bit over my head (for now), so this may be an incomplete answer, but I do have some insights that are waaay too long for the comments section.
Spring Design Stuff
The most important factors in designing a valve spring are going to be rate, free standing length (FL), coil bind (solid height), and stress. The amount of wire in the spring determines the rate (less wire = higher rate = higher stress), so wire Ø, coil count, and spring Ø are the dimensional factors that will effect rate.
Rate and FL, when combined with valve stem length, will allow you to calculate seat pressure. To increase seat pressure, you can increase FL or rate, both of which increase stress as the spring approaches solid height. Stress is a critically limiting factor in valve spring design, considering the extreme environment. For the sake of theoretical discussion, however, it does not matter, and will not be mentioned again. I will also ignore float, as that is fairly situational phenomenon.
Maximum valve lift is advised to be some number (say .050") over solid height of the spring so as not to break all of the things. Solid height is simply coil count * wire Ø.
1) Is there a correlation between seat pressure and valve lift? Yes and no, depending on your limitations. Given the above information, and keeping all other dimensional factors constant (FL, wireØ, coil count, springØ), there are only two individual dimensional changes to the spring that would effect both seat pressure AND valve lift:
- Increasing wire Ø would increase spring rate and therefore seat pressure, but also increase solid height, limiting valve lift. Wire Ø is calculated to the fourth power in the spring rate equation, so seat pressure would increase exponentially as the valve lift decreased.
- Decreasing the coil count would increase the spring rate, and again seat pressure, but would decrease the solid height, allowing more valve lift. Active coil has a linear relationship to rate, so seat pressure increases linearly with valve lift.
Note: All other individual changes to dimensional variables show no correlation. If you want to know the effect of changing multiple variables, it gets much more complicated, unless you have specific numbers to work with.
EDIT BASED ON COMMENTS
I wrote this answer from a spring design point of view, as if you were shopping for springs for your engine build. As per Paulster2's comment, a common way to increase seat pressure for the springs you already have is to install a shim between the cam lobe and spring body. Doing so will increase your seat pressure by some number of lbs (spring rate * shim height), and will also DECREASE your valve lift, as your new installed spring height is lower, bringing the spring closer to its solid height. So, to re-answer the question, if you are using a shim to increase seat pressure, valve lift with decrease linearly as seat pressure increases. See example below.
Say you have a 1.000" tall (unloaded FL) spring with a 100 lb/in rate, and your spring coil binds at .300". Right now, you install your spring at .800", which travels the spring .200 inches at 100 lbs/inch, for a seat pressure of 20 lbs. That means your remaining travel from installed height to solid height is .500", so in theory, your maximum valve lift is .499".
Now say you wanted to increase your seat pressure to 30 lbs. To do so, you install a .100" shim somewhere between the end of the spring and the cam lobe. This lowers the installed length of the spring to .700", giving you the 30 lb seat pressure you were looking for, but it also reduces the amount of travel between your installed length and solid height to .400", leaving you with a theoretical maximum valve lift of .399".
2) What are the differences between roller and tappet cam springs? I have no idea. I don't see why there would be a difference. I was thinking a roller would allow a higher seat pressure, but ideally you have the lowest seat pressure possible so as to more hastily allow air past the valve, so I don't see why you'd need different springs. Again, I could be wrong, please let me know if you have more specific questions.
3) What are the downsides of using a higher seat pressure than required?
As you mentioned, frictional losses, which increase heat in an already toasty environment. As you know, as heat increases (beyond a certain material specific point), the torsional rigidity of the wire will decrease, possibly causing yield, definitely causing a drop in seat pressure/rate. From a spring standpoint, higher than necessary seat pressure has no benefit, and not insignificant detriments.
We can also get into the discussion of valvetrain weight (and spring material), which, like suspension systems, will effect how quickly the spring can react to changes. Regardless of whether the valve is open or closed, the center coils in a valve springs are constantly moving when the engine is running due to the weight of the material in the spring.
Hopefully this answered some of your question(s). Please let me know if I can clarify, add to, answer additional, or delete this post!